# Brauer Lecture 2013

# The Alfred Brauer Lectures, March 4-6, 2013

# Vaughan Jones, Vanderbilt University and UC Berkeley

## "VON NEUMANN ALGEBRAS"

Von Neumann had many motivations from mathematics and physics in introducing what he called "Rings of operators" - certain algebras of operators on Hilbert space. I will give a definition suitable for those who remain shaky on the concept of Hilbert space, and explain how the subject has developed.

## Lecture 1: "WHAT IS......A VON NEUMANN ALGEBRA?" - Monday, March 4, 3:30-4:30 PM, Phillips Hall 215

## Lecture 2: "SUBFACTORS" - Tuesday, March 5, 4:00-5:00 PM, Phillips Hall 332

## Lecture 3: "SUBFACTORS AND EVERYTHING" - Wednesday, March 6, 4:00-5:00 PM, Phillips Hall 332

*There will be a reception in the Mathematics Faculty/Student Lounge on the third floor of Phillips Hall, Room 330, starting at 4:45 P.M. on Monday, March 4th. Refreshments will be available at 3:30 before the second and third lectures.*

**About the 2013 Brauer Lecturer: **

Vaughan Jones, Professor of Mathematics at Vanderbilt University and Emeritus Professor at UC Berkeley, is famous for his surprising discovery of the so-called Jones polynomial, a fundamental invariant in knot theory that arose from work in the apparently unrelated subject of Von Neumann algebras. This work has revolutionized the ancient subject of knots, and has led as well to new developments in physics and biology. It was no surprise when Jones was awarded the Fields Medal in 1990 at the International Congress of Mathematicians in Kyoto.

A native of New Zealand, Jones received his Docteur ès Sciences in Mathematics under André Haefliger at the University of Geneva in 1979. He came to the US in 1980, holding positions at UCLA and Penn before becoming Professor of Mathematics at the University of California at Berkeley in 1985. He has been Professor at Vanderbilt since 2011. Besides his Fields Medal, Jones has won the New Zealand Government Science Medal and the Onsager Medal. His honors include election as Fellow of the Royal Society and US National Academy of Sciences, and honorary membership in the London Mathematical Society. Long active on scientific advisory and editorial boards, he was in 2004 elected vice-president of the American Mathematical Society.

The Alfred Brauer Fund was established by the Department of Mathematics in 1984 on the occasion of Dr. Brauer’s ninetieth birthday, and the Alfred Brauer Lectures began in 1985. The most recent Brauer Lecturers have been Peter Sarnak, János Kollár, Andrew Majda, Jeff Cheeger, Shing-Tung Yau, Percy Deift, Charles Fefferman, Claire Voisin, Alex Eskin, Gérard Laumon, and Alexander Lubotzky.